Diphenylpolyene Dye Spectra
The purpose of this lab is to interpret uv-visible spectra of three
diphenyl polyenes. The uv-visible transitions are compared to a
particle-in-a-box model and to transitions calculated using timedependent density functional theory. A molecular vibration
frequency is extracted from vibrational structure.
Introduction
Figure 1: diphenyl polyenes
Phenyl-substituted polyenes include stilbene, which has a single C=C linking two phenyl rings;
the butadiene, hexatriene and octatetraene polyenes that are the subject of this lab; and longerchain polyenes. The diphenylpolyenes absorb uv-visible light strongly and fluoresce
significantly. In the photo-excited state, they may undergo cis-trans isomerization about the
linking polyene, so they have been used to study the fundamentals of isomerization kinetics and
to model visual pigments.
Absorption and fluorescence spectra of
diphenylbutadiene1 are shown at right. Spectra of the
larger polyenes are similar but red-shifted. The evident
vibronic structure has been attributed2,3 to a carboncarbon stretching vibration that has ag symmetry in the
molecule’s C2h point group. We will record
diphenylpolyene absorption spectra and then analyze
them with two models, the particle-in-a-box model4,5,6
and the time-dependent density functional (tddft)
quantum-chemical method.
dyespec_tddft.odt
Figure 2: Wallace­Williams, et al., J.
Phys. Chem. 1994, 98, 60­67
1
Theory
A simple approximation for an electronic transition is that it
arises from transfer of an electron from the highest occupied
molecular orbital (HOMO) of the molecule to the lowest
unoccupied molecular orbital (LUMO). One theory with
which the electronic transitions in diphenyl polyenes have
been treated is the particle-in-a-box model4-6. The electron
is the particle and the polyene is the box. The energy
difference between states ni and nf is
2
2
Δ E = (nf − ni )
h
2
Figure 3: box levels
2
8 me L
(1)
where h is Planck's constant (6.626×10-34 J·s) and me is the mass of an electron (9.109×10-31kg).
If ni is the quantum number of the HOMO, and nf the LUMO, then the energy gap is related to
the spectral wavelength by
ΔE =
hc
λ
(2)
where c is the speed of light, 2.998×108 m/s. The simple particle-in-a-box model correctly
predicts the most striking feature of diphenylpolyene spectra: they are displaced to longer
wavelengths as the length of the polyene increases.
The HOMO-LUMO energy gap could also be calculated from semi-empirical or ab initio
quantum-chemical theories.7 Equation 2 would still apply. However, considering only the
HOMO and the LUMO gives poor results. Excitation wavelengths obtained from many-electron
calculations will be poor unless electron-electron correlation is considered. Consequently, we
will use the time-dependent density functional method (tddft) when calculating wavelengths
quantum mechanically. The tddft method8 is a popular quantum-mechanical method for
calculating excitation energies.
dyespec_tddft.odt
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During the electronic excitation vibrations may also be excited. If
primarily one vibrational mode is excited then the electronic spectrum
will consist of several peaks separated by a constant energy difference.
The longest-wavelength peak corresponds to no vibrational excitation
and is referred to as the 0-0 transition. The energy difference between
successive peaks equals the vibrational energy (literally hc ν̃ ) of the
excited mode.
Figure 4: absorption peaks
ν̃ vib=
( λ1 − λ1 )
01
00
.
(3)
The vibration frequency obtained from equation 3 actually applies to
the first excited state of the diphenylpolyene molecule, S1 as indicated
in the sketch of potential energy surfaces at right.3 For this particular
carbon-carbon vibration, the frequency in the S1 excited state
approximately equals the frequency in the S0 ground state.
Figure 5: energy surfaces
Reagents and Supplies
•
5 mL 2×10-6M 1,4-diphenyl-1,3-butadiene in cyclohexane
•
5 mL 1×10-6M 1,6-diphenyl-1,3,5-hexatriene in cyclohexane
•
•
•
5 mL 1×10-6M 1,8-diphenyl-1,3,5,7-octatetraene in cyclohexane
a few mL cyclohexane to rinse cells
NOTE: cyclohexane is highly volatile, flammable, and irritating to breathe.
Keep solutions and cuvettes covered!
Dispose of samples and waste solutions in the proper waste bottle.
You will need a transfer pipet to transfer samples from the bottles to the cuvette. A glass
disposable pipet will do. You will need one or two clean glass or quartz (not plastic) cuvettes.
There may be cuvettes near the spectrometer.
dyespec_tddft.odt
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Procedure
Retrieve the dye solutions from the refrigerator or the hood. If they are frozen allow them to
thaw on the bench top or in warm water. (Cyclohexane solutions that quickly.)
Spectra may be recorded using the Cary 50 uv-visible spectrophotometer.
Instructions for taking spectra with the Cary 50 spectrophotometer
If it is not already running, open the Cary WinUV software.
Open the “Scan” program. The program will turn on the Cary
50 uv-visible spectrophotometer. After a minute or two,
commands can be given.
On the Setup menu, choose the following.
On the Cary tab
X mode 300 – 425 nm range
Y mode in Abs from -0.05 to 0.25
Beam mode dual beam
Cycle mode should be unselected
Scan speed slow either slow or slowest
On the Baseline tab
Baseline correction
On the main screen, click the “zero” button. “0.000” should
then be displayed in the upper-left corner.
Figure 6: Cary 50 spectrophotometer
Place a cuvette (glass or quartz) containing solvent (cyclohexane) in the cell holder. Click the
“Baseline” button to record the solvent's spectrum as a baseline. The Cary software will subtract
this baseline absorbance from all subsequent spectra.
Fill the cuvette with diphenylbutadiene dissolved in cyclohexane. Place it in the sample holder.
Click “Start” to record the spectrum. Use the vertical double-arrow icon to autoscale the y axis.
Use Peak labels, with “All peaks” selected, to label peaks. You may need to label some peaks by
hand. To do that, choose the cursor tool by clicking on the diagonal-left green-arrow icon.
Move the cursor to a peak. Then use the right mouse button to add a label.
You may save a spectrum as a spreadsheet-compatible csv file, as follows. On the File menu,
choose “Save data as...”. Then choose the file type “Spreadsheet Ascii (*.csv)” and check the
“Save only focused trace” box.
Take spectra of the other two dyes in the same way.
Include the spectra in your report.
dyespec_tddft.odt
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Experiment-Based Calculations
Make a table that contains the wavelengths of the peaks in your spectra. Record the two
longest-wavelength peaks (i.e., λ00 and λ01) in each compound's spectrum. Also convert
their wavelengths to wavenumbers (cm-1) and record those. Either include your spectra in
your report or attach them to your report. The dyes can degrade or be contaminated
during the semester, so watch out for spurious peaks.
The spacing between λ00 and λ01 is due to excitation of a carbon-carbon vibration. From
your spectral data, calculate the vibration frequency ν̃ (in wavenumbers) for each
compound.
Particle-in-Box-Based Calculations
Interpret the 0-0 transitions as those of polyene π electrons in one-dimensional boxes.

The average carbon-carbon bond length in a chain of alternating single and double
bounds is 139 pm. The length of the carbon chain between the phenyl rings is
L=(2j+1)X139pm, where j is the number of double bonds in the polyene chain (e.g., j=2
for diphenylbutadiene). Calculate L for each of the three dye molecules. Note that 1 pm
= 10-12 meters.

Each double bond contributes two π electrons. For diphenylbutadiene, the HOMO
corresponds to ni =2 and the LUMO to nf=3. Calculate the HOMO-LUMO ΔE for each
of the diphenylpolyenes, using equation 1.

From each ΔE calculate λ, using equation 2.

Compare the calculated particle-in-a-box λ values to the spectral λ00 values.
Time-Dependent Density-Functional Calculations
Following the procedure below, use GAMESS to calculate the dye molecules' equilibrium
geometry, and then the excitation energy of each molecule. The excitation energy can be
converted to wavelength (using λ = hc/ΔE), and that wavelength can be compared to your
observed λ00 values. Step-by-step instructions follow.
1. Draw the diphenylbutadiene
molecule.
2. Prepare a GAMESS input file to
optimize geometry using the
semiempirical method, AM1. The
AM1 method is approximate but fast.
Figure 7: diphenylbutadiene
dyespec_tddft.odt
5
It will optimize hydrocarbon bond lengths and angles to near-correct values. Key inputfile lines, other than coordinates, follow. OPTTOL=0.0006 is a loose geometryoptimization criterion, making convergence more likely than with the default 0.0001.
$CONTRL SCFTYP=RHF RUNTYP=OPTIMIZE $END
$BASIS GBASIS=AM1 $END
$STATPT OPTTOL=0.0006 NSTEP=500 $END
There sometimes is trouble getting the geometry optimization to converge. An error
message about being unable to calculate the Hessian, and suggesting changing
coordinates, is troublesome. These solutions have sometimes have given some success:
(1) re-orient the molecule along the x, y or z axis, (2) flatten the molecule, and (3) specify
the “rational function” optimization method by inserting METHOD=RFO in the STATPT
command line.
3.
Run a TDDFT calculation to determine the energy required to excite the molecule from
its ground state. Use density functional theory, the B3LYP functional and the 6-31G(d)
basis set. TDDFT is used for this step because it is one of the few methods able to
calculate energies of excited states. It is slow, however. One may expect this step to
require one-half to one hour. (Note: choosing RUNTYP "OPTIMIZE" rather than
"ENERGY" will greatly extend the calculation time and is not recommended.) Here are
key input lines. $CONTRL SCFTYP=RHF RUNTYP=ENERGY DFTTYP=B3LYP TDDFT=EXCITE MAXIT=50 $END
$BASIS GBASIS=N31 NGAUSS=6 NDFUNC=1 $END
$SYSTEM MWORDS=32 $END
The CONTRL line specified a TDDFT calculation using the B3LYP functional. The
basis-set line is routine. The $SYSTEM line allocates 32 megawords of memory. That
allocation is optional. The DATA section is not shown. It contains the AM1-optimized
coordinates of the molecule.
When the calculation is done, look for “SINGLET EXCITATIONS” near the end of the
output file. Both state energies and ΔE will be in the file. Either use the ΔE that is given
or calculate ΔE from ground- and excited-state energies. eV = 1.602X10-19 Joules.
4.
Calculate λ from hc/ΔE. Compare λ to your experimental λ00.
5. Repeat the above steps for diphenylhexatriene and diphenyloctatetraene. Calculating
excitation energy is difficult with any routine theory, including tddft, so wavelength
errors of 20 to 40 nm are not unusual. However, tddft (or almost any theory) should
reproduce the trend of increasing excitation wavelength with increasing molecular size.
dyespec_tddft.odt
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References
1. Wallace-Williams, S.E.; Schwartz, B.J.; Moller, S.; Goldbeck, R.A.; Yee, W.A.; El-Bayoumi,
M.A.; Kliger, D.S. Excited state spectra and dynamics of phenyl-substituted butadienes.
Journal of Physical Chemistry 1994, 98, 60-67.
2. Zerbetto, F.; Zgierski, M.Z. On the 1Ag → 1Bu absorption spectrum of four butadiene
isotopomers. Chemical Physics Letters 1989, 157, 515-520.
3. Mustroph, H.; Reiner, K.; Mistol, J.; Ernst, S.; Dietmar, K.; Hennig, L. Relationship between
the molecular structure of cyanine dyes and the vibrational fine structure of their electronic
absorption spectra. ChemPhysChem 2009, 10, 835-840.
4. Anderson, B. D. Alternative compounds for the particle in a box experiment. Journal of
Chemical Education 1997, 74, 985.
5. Engel, T.; Reid, P.; Hehre, W. Physical Chemistry, Third Edition, Person Education: Boston,
2013. The particle-in-a-box model is applied to uv-visible transitions of pi electrons in
Section 16.3. Vibrational transitions that accompany electronic transitions are discussed in
Sections 25.4 and 25.5.
6. Autschbach, Jochen Why the particle-in-a-box model works well for cyanine dyes but not for
conjugated polyenes. Journal of Chemical Education 2007, 84(11), 1840-1845.
7. Cao, J.; Wu, T.; Hu, C.; Tao, L.; Sun, W.; Fan, J.; Peng, X. The nature of the different
environmental sensitivity of symmetrical and unsymmetrical cyanine dyes: an experimental
and theoretical study. Physical Chemistry Chemical Physics, 2012, 14, 13702-13708.
8. Cramer, C. J. Essentials of Computational Chemistry: Theories and Models; John Wiley &
Sons: New York, 2002; page 136.
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